The Titian-haired model-turned-Cambridge grad has been snapped getting close to the billionaire tech guru as they spent the New Year’s break holidaying together on luxury yacht the Odessa – which reportedly costs an exorbitant $240K to charter per week – in St. Barts.

The duo have been snapped laughing, chatting and cuddling up to one another, going for meals at local hot spot L’Isoletta and the 25-year-model was also photographed slathering sun cream on 36-year-old entrepreneur Jack’s back.

Cole has also been spending her downtime paddle-boarding, walking along the beach, going for swims and lounging on the super-yacht.

The two have been holidaying with other A-listers including Def Jam Records founder Rick Rubin and Oscar-winning producer Brian Grazer.

Judging by Cole’s latest Twitter postings, the model certainly seems to be in a loved-up frame of mind. Cole posted a pic of herself in a bandeau bikini top and Santa hat on Christmas Day captioned: ‘Accidentally holding the moon,’ and followed up with the floaty posts: ‘it takes two wings to fly’ and ‘A rainbow exploded in my dream last night’ on New Year’s Eve.

Good thing that ‘hot new couple’ easily fits into less than 140 characters.

What do you think of Lily Cole’s rumoured new beau? Let us know in a comment below.